Someone told me that in Romania, if you mistakenly call someone by a different name, you owe that person a lamb.

It is a figure of speech. You gave a person another name.
In Romanian tradition, when somebody gives another a new name, becomes a Godparent.
As a rule a Godparent gives the child presents. Long time ago used to be a lamb (sheep).
There for, you owe a person a lamb on a BBQ next to a cooler full of cold beer.